Conceptual Question on Rolling Objects

[JProffitt71]

Okay, so I am somewhat new to physics (finishing up my first Mechanics/EM course), and I often get stuck on concepts until they make sense to me intuitively. Everything to do with translational motion made sense instantaneously, and I have powered through EM, but I have always struggled with rotational motion, and the physics behind any object rolling down a ramp without slipping has been eluding me all year. I understand mathematically that the sum of the forces upon the ball along the ramp is equal to mgsin(theta) minus some frictional force, and I can solve for that frictional force with the non-slipping relations between translational and rotational motion. However, I have yet to figure out what the hell that force is and what it does to the ball's motion, conceptually.

I do know that it resists the gravitational force, and varies directly with the coefficient of its rotational inertia, which makes sense. I know also that it is what rolls the ball, being a force displaced from its center of mass, otherwise I couldn't solve for it. However, I run into a problem when I consider how exactly the ball is moving down the ramp. Gravity is acting on the entire ball, pulling it down the ramp and friction seems to be resisting, but friction makes the ball roll, making it go down the ramp if there's no slippage.

This becomes a problem when I ask myself what happens when the coefficient of friction on the ramp is increased. Does the ball roll down slower due to the extra resistance, or faster with the extra torque, or neither? What happens when I change other things and why, without using equations? I can solve for all of this given enough time, but if that is limited and I don't have a feel for what that ball (or any rotating object) should do, things could get quite stressful.

It all makes sense on a very strictly mathematical level, but I cannot picture it happening in my head like I can nearly everything else. So, if you have any insights on any part of how rolling objects accelerate the way they do down ramps, I would greatly appreciate it. And if not, that's okay too, my approach is kinda weird and sometimes math will be the only way (I can think of it as rotational KE and translational KE, but that doesn't help me visualize it very well)

 

[timthereaper]

Okay, I think I understand your question. If not, let me know. For a ball rolling down the ramp without slipping, the ball must be going the same speed as the ramp at the point of contact (that's just a basically a restatement of the no-slip condition). That means at the point of contact, the force exerted on the ramp by the ball at that point is equal to the friction force exerted by the ramp on the ball (forces cancel at the point of contact). Because the forces cancel, there is no motion of the ball's surface along the ramp. If you want to think of it this way, that point is an instant center of rotation, where the ball is technically rotating about the point of contact at that instant. Gravity is still acting on the other parts of the ball and makes the ball rotate. That's how friction causes rolling in this case.

When the forces of friction and gravity don't cancel at the point of contact, you get slip. You can imagine throwing the same ball along a sheet of ice. If you throw it with enough speed, the ball will slide along the ice sheet because at point of contact the force due to friction won't cancel the force that the ball is exerting on the ice. When the ball slows down enough, the forces will cancel and then the ball will roll instead of sliding.

 

[Naty1]

"This becomes a problem when I ask myself what happens when the coefficient of friction on the ramp is increased."

nothing: the ball either slips while rolling or the frictional forces act equally as Tim says above.

On the other hand, if a ball is thrown down an incline, having some linear and some rotational motion, an incline with greater friction will cause the ball to begin rotating sooner.

But you might be able to envision a "velcro" type of unusual sticky friction where if the ball and incline are both "sticky", the ball would be slowed down or stopped...but that's not typical "friction and maybe another name applies.

 

[Doc Al]

Gravity is acting on the entire ball, pulling it down the ramp and friction seems to be resisting, but friction makes the ball roll, making it go down the ramp if there's no slippage.

Without friction, the ball will slide down the ramp without rotating. Friction opposes the slipping between the surfaces, exerting a torque on the ball that causes it to rotate. That rotation comes at the expense of translational energy: since friction acts opposite to the translational motion, it reduces the translational acceleration.

This becomes a problem when I ask myself what happens when the coefficient of friction on the ramp is increased. Does the ball roll down slower due to the extra resistance, or faster with the extra torque, or neither?

What makes you think that the frictional force increases when the coefficient of friction is increased? The friction--which is static friction--will be whatever it needs to be to prevent slipping. (What the coefficient of friction determines is the maximum amount of friction you can get for a given normal force--but you know you already have enough if it's able to roll without slipping.)

 

[Doc Al]

That means at the point of contact, the force exerted on the ramp by the ball at that point is equal to the friction force exerted by the ramp on the ball (forces cancel at the point of contact). Because the forces cancel, there is no motion of the ball's surface along the ramp.

Maybe I'm not understanding your point here. The force that the ball exerts on the ramp will always be equal and opposite to the force that the ramp exerts on the ball, regardless of whether the ball slips or not. They are third law pairs--and they act on different objects.

 

[timthereaper]

Doc Al, I guess I phrased or worded that wrong. I just meant that for the ball to slide on the ramp the part of the ball in contact has to produce a force greater than the maximum friction force. Come to think of it, maybe I worded this reply badly too. I hope you get what I mean.

 

[Doc Al]

Doc Al, I guess I phrased or worded that wrong. I just meant that for the ball to slide on the ramp the part of the ball in contact has to produce a force greater than the maximum friction force. Come to think of it, maybe I worded this reply badly too. I hope you get what I mean.

Here's how I would put it. If the amount of friction force required to prevent slipping exceeds the available static friction, then the ball will begin to slip.

 

[timthereaper]

Hahaha yeah, that sounds about right.